The lines make the sum total of "The Chanty of the Sea-Cook," from the story "A Schooner-Errant," by Percie W. Hart, published in 1898.

Hart almost certainly wrote it for the story, as follows:

A full-rigged ship is a r'yal queen,
    Way-ho for Boston town-o !
A lady o' court is a barkentine,   
    An' now our anchor's down-o'.
A bark is a gal with ringlets fair,
A brig is the same, with shorter hair,
A top-sail craft is a racing mare,   
    But a schooner, she's a clown-o!

The suggestion that it's a genuine shanty is belied by the implication that sailors would sing when *letting go* the anchor.
And there's the whole literary-metaphorical thing.

The "town-os" and "down-os" lead me to guess that Hart was thinking of "The Fox Went Out on a Moonlit Night" as he wrote the words. Any good Mudcatter with a mind to sing should be able to adapt the tune.